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Mathematics, 17.04.2020 06:06 Katlyndavis01
Identify the proof to show that △LMQ≅△NPQ, where Q is the midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯, ∠L≅∠N, and LM¯¯¯¯¯¯≅NP¯¯¯¯¯.
The figure shows two triangles L M Q and N P Q. The triangles have a common vertex Q. Points M, Q, P lie on one line. Points N, Q, L lie on one line.
1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅QP¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠P (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)
1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (third angles theorem)6. ∠M=∠P (vertical angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)
1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠P (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)
1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠N (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)
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Identify the proof to show that △LMQ≅△NPQ, where Q is the midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯, ∠L≅∠N, a...
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